Finite Group DatabasebetaFinite Group Databasebeta| order | 11132 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C121 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic23⋊C121 |
| unambiguous semidirect product | (C23⋊C121)⋊C4 |
| derived, Sylow | C23 ⋊ C4×C121 |
| Hall | C23⋊C121 ⋊ C4 |
| Hall | Dic23 ⋊ C121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C11 | AGL(1,𝔽23) |
| commutator, hypocenter | C23 | C4×C121 |
| Fitting, socle, prime radical, cosocle | C2×C11×C23 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C11 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,23,2,11|a^2=d,b^11=e,c^a=c^22,c^b=c^2506 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic23⋊C121, C3⋊(Dic23⋊C121) |
| maximal normal subgroup of | C3×Dic23⋊C121 |
| maximal quotient of | C3×Dic23⋊C121, C3⋊(Dic23⋊C121) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11132, 2);